Search NASA⌕ Search

SEARCH · Search NASA

Results for “linear projection”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Linear ion-scale microstability analysis of high and low-collisionality NSTX discharges and NSTX-U projections

Linear gyrokinetic simulations were conducted to investigate ion-gyroradius-scale micro-instability predictions for high-beta NSTX discharges and NSTX-U projections that span over an order of magnitude variation in collisionality. A complex mix of microtearing modes and hybrid trapped electron modes/kinetic ballooning modes (TEM/KBM) is predicted for all experimental or projected conditions. Ion temperature gradient (ITG) instabilities are typically stable in the NSTX discharges investigated, consistent with the observed neoclassical ion thermal transport. ITG thresholds inferred from the simulations are typically much higher than the experimental NSTX gradients, as well as the projected gradients in the NSTX-U scenario, which assumed ion temperatures limited by neoclassical transport only. The analysis suggests ITG instabilities are unlikely to contribute significant anomalous thermal losses in high-beta, lower collisionality NSTX-U scenarios. On the other hand, the NSTX experimental profiles and NSTX-U projections are predicted to be very close to the predicted onset of unstable KBM at most radii investigated. The proximity of the various discharges to the KBM instability threshold implies it may play an important role in setting profile shapes and limiting global energy confinement. Here, it remains to be understood and predicted how KBM contributes to multi-channel transport (thermal and particle transport, for both ions and electrons) in a way that is consistent with experimental inferences.

36 MATERIALS SCIENCE↗
NASA NTRS1992

Computational algorithms for increased control of depth-viewing volume for stereo three-dimensional graphic displays

Three-dimensional pictorial displays incorporating depth cues by means of stereopsis offer a potential means of presenting information in a natural way to enhance situational awareness and improve operator performance. Conventional computational techniques rely on asymptotic projection transformations and symmetric clipping to produce the stereo display. Implementation of two new computational techniques, as asymmetric clipping algorithm and piecewise linear projection transformation, provides the display designer with more control and better utilization of the effective depth-viewing volume to allow full exploitation of stereopsis cuing. Asymmetric clipping increases the perceived field of view (FOV) for the stereopsis region. The total horizontal FOV provided by the asymmetric clipping algorithm is greater throughout the scene viewing envelope than that of the symmetric algorithm. The new piecewise linear projection transformation allows the designer to creatively partition the depth-viewing volume, with freedom to place depth cuing at the various scene distances at which emphasis is desired.

Williams, Steven P.↗
NASA NTRS2003

Linear optics and projective measurements for fun and profit

The technique of projective measurements in linear optics can provide an apparent, efficient nonlinear interaction between photons, which is technically problematic otherwise. We present an application of such a technique to prepare large photon-number path entanglement.

linear↗
DOE OSTI2020

Novel Geometric Operations for Linear Programming

This report summarizes the work performed under the project "Linear Programming in Strongly Polynomial Time." Linear programming (LP) is a classic combinatorial optimization problem heavily used directly and as an enabling subroutine in integer programming (IP). Specifically IP is the same as LP except that some solution variables must take integer values (e.g. to represent yes/no decisions). Together LP and IP have many applications in resource allocation including general logistics, and infrastructure design and vulnerability analysis. The project was motivated by the PI's recent success developing methods to efficiently sample Voronoi vertices (essentially finding nearest neighbors in high-dimensional point sets) in arbitrary dimension. His method seems applicable to exploring the high-dimensional convex feasible space of an LP problem. Although the project did not provably find a strongly-polynomial algorithm, it explored multiple algorithm classes. The new medial simplex algorithms may still lead to solvers with improved provable complexity. We describe medial simplex algorithms and some relevant structural/complexity results. We also designed a novel parallel LP algorithm based on our geometric insights and implemented it in the Spoke-LP code. A major part of the computational step is many independent vector dot products. Our parallel algorithm distributes the problem constraints across processors. Current commercial and high-quality free LP solvers require all problem details to fit onto a single processor or multicore. Our new algorithm might enable the solution of problems too large for any current LP solvers. We describe our new algorithm, give preliminary proof-of-concept experiments, and describe a new generator for arbitrarily large LP instances.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Corrosion of Containment Alloys in Molten Salt Reactors and the Prospect of Online Monitoring

The aim of this review is to communicate some essential knowledge of the underlying mechanism of the corrosion of structural containment alloys during molten salt reactor operation in the context of prospective online monitoring in future MSR installations. The formation of metal halide species and the progression of their concentration in the molten salt do reflect containment corrosion, tracing the depletion of alloying metals at the alloy salt interface will assure safe conditions during reactor operation. Even though the progress of alloying metal halides concentrations in the molten salt do strongly understate actual corrosion rates, their prospective 1 st order kinetics followed by near-linearly increase is attributed to homogeneous matrix corrosion. The service life of the structural containment alloy is derived from homogeneous matrix corrosion and near-surface void formation but less so from intergranular cracking (IGC) and pitting corrosion. Online monitoring of corrosion species is of particular interest for molten chloride systems since besides the expected formation of chromium chloride species CrCl 2 and CrCl 3 , other metal chloride species such as FeCl 2 , FeCl 3 , MoCl 2 , MnCl 2 and NiCl 2 will form, depending on the selected structural alloy. The metal chloride concentrations should follow, after an incubation period of about 10,000 hours, a linear projection with a positive slope and a steady increase of <1 ppm per day. During the incubation period metal concentration show 1 st order kinetics and increasing linearly with time. Ideally, a linear increase reflects homogeneous matrix corrosion, while a sharp increase in the metal chloride concentration could set a warning flag for potential material failure within the projected service life, e.g. as result of intergranular cracking or pitting corrosion. Continuous monitoring of metal chloride concentrations can therefore provide direct information about the mechanism of the ongoing corrosion scenario and offer valuable information for a timely warning of prospective material failure.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS2013

A Turn-Projected State-Based Conflict Resolution Algorithm

State-based conflict detection and resolution (CD&R) algorithms detect conflicts and resolve them on the basis on current state information without the use of additional intent information from aircraft flight plans. Therefore, the prediction of the trajectory of aircraft is based solely upon the position and velocity vectors of the traffic aircraft. Most CD&R algorithms project the traffic state using only the current state vectors. However, the past state vectors can be used to make a better prediction of the future trajectory of the traffic aircraft. This paper explores the idea of using past state vectors to detect traffic turns and resolve conflicts caused by these turns using a non-linear projection of the traffic state. A new algorithm based on this idea is presented and validated using a fast-time simulator developed for this study.

Butler, Ricky W.↗
NASA NTRS1994

Deep VLA imaging of twelve extended 3CR quasars

A representative sample of 12 extended quasars from the 3CR catalog has been imaged at 4.9 GHz using the Very Large Array (VLA). These full synthesis observations typically achieve an rms noise of 20 micro-Jy per beam. Jets are detected on at least one side of every source. The jets are well collimated compared with those in less powerfull sources, but spreading is detected in most of them. The opening angles of several jets are not constant, but show recollimation after an initial regime of rapid spreading. Many of the jets contain quasiperiodic strings of knots, of which the knot closest to the central feature is usually the brightest (until the jet nears its hot spot). The degrees of linear polarization at the jet knots range from less than 5% to approx. 50%, but show no common trend with distance along the jets. In knots that are elongated in directions close to that of the jet, the E vectors tend to be orthogonal to the jet axis. The prominence of the inner, straighter jet segments relative to the extended lobes correlates significantly with the prominence of the milliarcsecond-scale central features, but the prominence of the more bent jet segments does not. Candidates for counterjet emission are detected in seven sources, but there is no unambiguous, continuous counterjet in any of them. Estimates of the flux density ratios between the straighter jet segments and the counterjets based on these tentative detections range from 1.2:1 to greater than 175:1. There is no evidence in this sample that counterjet detectability correlates with such putative inclination indicators as central feature prominence or projected linear size. There is also no evidence that the prominence of the counterjets anticorrelates with that of the jets as predicted by simple relativistic-beaming models for the jet/counterjet asymmetry. There is, however, strong evidence that large bends in the main jet favor counterjet detection, and there are no counterjet candidates opposite long, uninterrupted straight segments of the main jets. The detectability of the counterjets in these quasars may therefore be strongly influenced by interactions between the underlying beams and inhomogeneities in the surrounding material. We offer a new empirical definition of the term 'hot spot' that is intended to improve the distinction between such features and 'jet knots.' Both the compactness of hot spots and their position in the lobe are affected by whether they are fed by a detectable jet. When the hot spots differ significantly in compactness, the more compact one is always on the jetted side. Jetted hot spots are also more likely to be recessed deeply from the outer edge of their lobes than are their counterjetted counterparts. The jetted hot spot is less prominent relative to other extended emission if the jet bends through a large angle, particularly if a large bend occurs abruptly. The counterjetted hot spot is also less well defined if the jet is more bent. The lobes of several sources show considerable inhomogeneity, including filamentation.

Bridle, Alan H.↗
DOE OSTI2022

Variational encoder geostatistical analysis (VEGAS) with an application to large scale riverine bathymetry

Estimation of riverbed profiles, also known as bathymetry, plays a vital role in many applications, such as safe and efficient inland navigation, prediction of bank erosion, land subsidence, and flood risk management. The high cost and complex logistics of direct bathymetry surveys, i.e, depth imaging, have encouraged the use of indirect measurements such as surface flow velocities. However, estimating high-resolution bathymetry from indirect measurements is an inverse problem that can be computationally challenging. Here, we propose a reduced-order model (ROM) based approach that utilizes a variational autoencoder (VAE), a type of deep neural network with a narrow layer in the middle, to compress bathymetry and flow velocity information and accelerate bathymetry inverse problems from flow velocity measurements. In our application, the shallow-water equations (SWE) with appropriate boundary conditions (BCs), e.g., the discharge and/or the free surface elevation, constitute the forward problem, to predict flow velocity. Then, ROMs of the SWEs are constructed on a nonlinear manifold of low dimensionality through a variational encoder and the bathymetry inversion problem is derived on the low-dimensional latent space in a Hierarchical Bayesian setting. Further, the reformulation allows variational inference with a small number (e.g., $\mathscr{O}$ (100) of ROM runs and efficient uncertainty quantification. We have tested our inversion approach on a one-mile reach of the Savannah River, GA, USA. Once the neural network is trained (offline stage), the proposed technique can perform the inversion operation orders of magnitude faster than traditional inversion methods that are commonly based on linear projections, such as principal component analysis (PCA), or the principal component geostatistical approach (PCGA). Furthermore, tests show that the algorithm can estimate the bathymetry with good accuracy even with sparse flow velocity measurements.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

$\text{GPLaSDI}$: Gaussian Process-based interpretable Latent Space Dynamics Identification through deep autoencoder

Numerically solving partial differential equations (PDEs) can be challenging and computationally expensive. This has led to the development of reduced-order models (ROMs) that are accurate but faster than full order models (FOMs). Recently, machine learning advances have enabled the creation of non-linear projection methods, such as Latent Space Dynamics Identification (LaSDI). LaSDI maps full-order PDE solutions to a latent space using autoencoders and learns the system of ODEs governing the latent space dynamics. By interpolating and solving the ODE system in the reduced latent space, fast and accurate ROM predictions can be made by feeding the predicted latent space dynamics into the decoder. In this paper, we introduce GPLaSDI, a novel LaSDI-based framework that relies on Gaussian process (GP) for latent space ODE interpolations. Using GPs offers two significant advantages. First, it enables the quantification of uncertainty over the ROM predictions. Second, leveraging this prediction uncertainty allows for efficient adaptive training through a greedy selection of additional training data points. This approach does not require prior knowledge of the underlying PDEs. Consequently, GPLaSDI is inherently non-intrusive and can be applied to problems without a known PDE or its residual. Here we demonstrate the effectiveness of our approach on the Burgers equation, Vlasov equation for plasma physics, and a rising thermal bubble problem. Our proposed method achieves between 200 and 100,000 times speed-up, with up to 7% relative error.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Data-driven learning of Mori–Zwanzig operators for isotropic turbulence

Developing reduced-order models for turbulent flows, which contain dynamics over a wide range of scales, is an extremely challenging problem. In statistical mechanics, the Mori–Zwanzig (MZ) formalism provides a mathematically exact procedure for constructing reduced-order representations of high-dimensional dynamical systems, where the effects due to the unresolved dynamics are captured in the memory kernel and orthogonal dynamics. Turbulence models based on MZ formalism have been scarce due to the limited knowledge of the MZ operators, which originates from the difficulty in deriving MZ kernels for complex nonlinear dynamical systems. In this work, we apply a recently developed data-driven learning algorithm, which is based on Koopman's description of dynamical systems and Mori's linear projection operator, on a set of fully resolved isotropic turbulence datasets to extract the Mori–Zwanzig operators. With data augmentation using known turbulence symmetries, the extracted Markov term, memory kernel, and orthogonal dynamics are statistically converged and the generalized fluctuation–dissipation relation can be verified. The properties of the memory kernel and orthogonal dynamics, and their dependence on the choices of observables are investigated to address the modeling assumptions that are commonly used in MZ-based models. A series of numerical experiments are then constructed using the extracted kernels to evaluate the memory effects on prediction. The results show that the prediction errors are strongly affected by the choice of observables and can be further reduced by including the past history of the observables in the memory kernel.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A spatially resolved spectral analysis of giant radio galaxies with MeerKAT

ABSTRACT In this study we report the spatially resolved, wideband spectral properties of three giant radio galaxies (GRGs) in the COSMOS field: MGTC J095959.63+024608.6, MGTC J100016.84+015133.0, and MGTC J100022.85+031520.4. One of these galaxies, MGTC J100022.85+031520.4, is reported here for the first time, with a projected linear size of 1.29 Mpc at a redshift of 0.1034. Unlike the other two, it is associated with a brightest cluster galaxy (BCG), making it one of the few GRGs known to inhabit cluster environments. We examine the spectral age distributions of the three GRGs using new MeerKAT UHF-band (544–1088 MHz) observations, and L-band (900–1670 MHz) data from the MeerKAT International GHz Tiered Extragalactic Exploration (MIGHTEE) survey. We test two models of spectral ageing, the Jaffe–Perola and Tribble models, using the Broadband Radio Astronomy Tools (brats) software, and find that they agree well with each other. We estimate the Tribble spectral age for MGTC J095959.63+024608.6 as 68 Myr, for MGTC J100016.84+015133.0 as 47 Myr, and for MGTC J100022.85+031520.4 as 67 Myr. We find significant disagreements between these spectral age estimates and the estimates of the dynamical ages of these GRGs, modelled in cluster and group environments. Our results highlight the need for additional processes that are not accounted for in either the dynamic age or the spectral age estimations.

Charlton, K. K. L. (ORCID:0000000229252047)↗
DOE OSTI2023

Verifying the Computational Integrity of Power Grid Controls with Zero-Knowledge Proof

The control of future power grids is migrating from a centralized to a distributed/decentralized scheme to enable a massive penetration of distributed energy resources with rising dependence on communication infrastructure. A common assumption made for most existing distributed/decentralized controllers is that local controllers would faithfully follow the designated controller dynamics based on the data received from communication channels. However, with increased probability of cyberattacks on Operational Technology infrastructure, such an assumption could be risky because proper execution of the controller dynamics is then built on trust in secure communication and computation. In this work, we leverage a cryptography technology known as zero-knowledge scalable transparent arguments of knowledge (zk-STARK) to verify the computational integrity of power grid control algorithms, with projected linear dynamics-based control schemes as the initial proof-of-concept test case. The method presented here converts the cybersecurity challenge of data integrity for grid control into a subset of computational integrity.

computational integrity↗
DOE OSTI2021

Data-Driven Learning for the Mori--Zwanzig Formalism: A Generalization of the Koopman Learning Framework

A theoretical framework which unifies the conventional Mori--Zwanzig formalism and the approximate Koopman learning of deterministic dynamical systems from noiseless observation is presented. In this framework, the Mori--Zwanzig formalism, developed in statistical mechanics to tackle the hard problem of construction of reduced-order dynamics for high-dimensional dynamical systems, can be considered as a natural generalization of the Koopman description of the dynamical system. We next show that, similar to the approximate Koopman learning methods, data-driven methods can be developed for the Mori--Zwanzig formalism with Mori's linear projection operator. We have developed two algorithms to extract the key operators, the Markov and the memory kernel, using time series of a reduced set of observables in a dynamical system. We have adopted the Lorenz `96 system as a test problem and solved for the above operators. These operators exhibit complex behaviors, which are unlikely to be captured by traditional modeling approaches in Mori--Zwanzig analysis. The nontrivial generalized fluctuation-dissipation relationship, which relates the memory kernel with the two-time correlation statistics of the orthogonal dynamics, was numerically verified as a validation of the solved operators. Here we present numerical evidence that the generalized Langevin equation, a key construct in the Mori--Zwanzig formalism, is more advantageous in predicting the evolution of the reduced set of observables than the conventional approximate Koopman operators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Compact Steep Spectrum Radio Sources with Enhanced Star Formation Are Smaller Than 10 kpc

Compact steep spectrum (CSS) radio sources are active galactic nuclei (AGN) that have radio jets propagating only on galactic scales, defined as having projected linear size (LS) of up to 20 kpc. CSS sources are generally hosted by massive early-type galaxies with little ongoing star formation; however, a small fraction are known to have enhanced star formation. Using archival data from the Faint Images of the Radio Sky at Twenty cm survey, the Very Large Array Sky Survey, and the Sloan Digital Sky Survey, we identify a volume-limited sample of 166 CSS sources at z < 0.2 with L 1.4 GHz > 10 24 W Hz -1 . Comparing the star formation rates and linear sizes of these CSS sources, we find that the ≈14% of CSS sources with specific star formation rates above 0.01 Gyr -1 all have LS < 10 kpc. We discuss the possible mechanisms driving this result, concluding that it is likely the excess star formation in these sources occurred in multiple bursts and ceased prior to the AGN jet being triggered.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1979

Supernovae - A new selection effect

A sample of 228 supernovae that occurred in galaxies with known redshifts is used to show that the mean projected linear supernova distance from the center of the parent galaxy increases with increasing redshift. This effect is interpreted as an observational bias: the discovery rate of supernovae is reduced in the inner parts of distant, poorly resolved galaxies. Even under the optimistic assumption that no selection effects work in galaxies closer than 33 Mpc, about 50% of all supernovae are lost in the inner regions of galaxies beyond 150 Mpc. This observational bias must be taken into account in the derivation of statistical properties of supernovae.

Shaw, R. L.↗
NASA NTRS1987

Superluminal motion in the double-lobed quasar 3C 245

VLBI observations of 3C 245 obtained at 10.7 GHz with the Mark III array at five epochs in 1981-1986 are reported. The data-reduction and model-fitting procedures are explained, and the results are presented in tables, graphs, and maps along with previously published data on 11 other superluminal sources. The central component of the quasar is found to have an apparent transverse velocity of (3.1 + or - 1.4) c/h, assuming H0 = 100h km/s Mpc and q0 = 0.5. From the apparent source orientation (based on R, variability, apparent curvature, and projected linear size) it is inferred that the apparent transverse velocity is anticorrelated with the angle to the line of sight, as predicted by relativistic-beaming models of superluminal motion.

Hough, D. H.↗
NASA NTRS1988

Infrared spectroscopy, imaging, and 10 micron photometry of Giclas 29-38

An NIR spectrum and several images of Giclas 29-38, a white dwarf suspected to have a brown dwarf in orbit around it, are presented. There is no absorption feature in the spectrum that is deeper than 5 percent in the wavelength range 1.95-2.45 microns, from which it is inferred that there is no feature deeper than 10 percent at 2.4 microns from any brown dwarf companion. The IR spectrum does not yield any strong constraint on whether or not the thermal emission observed from G29-38 comes from a brown dwarf or dust. The 1.6- and 2.2-micron images of G29-38 appear indistinguishable from a point source with an upper limit of 0.4 arcsec for the separation of the white dwarf and the source of the excess IR emission. This corresponds to a projected linear separation of 5.6 AU. A 2sigma limit at 10 microns of 10 mJy constrains possible alternative models for the IR excess by emission from dust grains. While the present results do not show evidence for the suspected brown dwarf companion around G29-38, the presence of such an object cannot be ruled out.

Tokunaga, A. T.↗